Effect of Coulomb correlation on charge transport in disordered organic semiconductors

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Supplemental Material:

Effect of Coulomb correlation on charge transport in disordered organic

semiconductors

Feilong Liu,1,∗ _{Harm van Eersel,}2 _{Bojian Xu,}3 _{Janine G. E. Wilbers,}3 _{Michel P. de Jong,}3

Wilfred G. van der Wiel,3 _{Peter A. Bobbert,}1, 3, 4 _{and Reinder Coehoorn}1, 4

1

Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

2_{Simbeyond B.V., P.O. Box 513, 5600 MB Eindhoven, The Netherlands} 3_{NanoElectronics Group, MESA+ Institute for Nanotechnology,}

University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

4_{Institute for Complex Molecular Systems, Eindhoven University of Technology,}

P.O. Box 513, 5600 MB Eindhoven, The Netherlands

In this Supplemental Material, a comparison is given be-tween the mobility as studied using ME and KMC sim-ulations as a function of the electric field (Fig. S1), the charge carrier density (Fig. S2) and the relative dielec-tric constant (Figs. S3 and S4), for sets of simulation parameters that extend those in Figs. 1−3 in the main text. In all figures, the dashed curves give the mobility

as predicted using the parametrization scheme presented in Section III.B. A discussion of the simulation results is given in the last paragraph of Section III.B.

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FIG. S1. Calculated charge-carrier mobility µ as a function of the electric field F , at various charge-carrier concentrations c, for various disorder strengths σ at a fixed temperature T = 290 K (left) and for various temperatures at a fixed disorder strength σ = 0.1 eV (right). The three cases studied in each panel correspond to

relative disorder strengths ˆσ = σ/(kBT ) equal to 3, 4, and 6. All simulations were performed for εr= 3. Solid

curves: ME results (µME). Symbols: KMC results (µKMC). Dashed curves: µMEmultiplied by the empirical

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FIG. S2. Calculated charge-carrier mobility µ as a function of the carrier concentration c, for various disorder strengths σ at a fixed temperature T = 290 K (left) and for various temperatures at a fixed disorder strength σ = 0.1 eV (right). The three cases studied in each panel correspond to relative disorder strengths ˆσ = σ/(kBT )

equal to 3, 4, and 6. All simulations were performed for εr = 3. Solid curves: ME results (µME). Symbols: KMC

results (µKMC). Dashed curves: µME multiplied by the empirical mobility reduction factor given by Eqs. (1)−(3) in

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FIG. S3. Calculated charge-carrier mobility µ as a function of the relative dielectric constant εr at various charge

carrier concentrations c and disorder strenghts σ, at F = 107 (left) and F = 4 × 107V/m (right). All simulations were carried out for T = 290 K. Solid curves: ME results (µME). Symbols: KMC results (µKMC). Dashed curves:

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FIG. S4. Calculated charge-carrier mobility µ as a function of the relative dielectric constant εr at various charge

carrier concentrations c and temperatures T , for F = 107 _{(left) and F = 4 × 10}7 _{V/m (right). All simulations were}

carried out for a fixed disorder strength σ = 0.1 eV. Solid curves: ME results (µME). Symbols: KMC results (µKMC).